How do you find the domain and range for #y = 2/(x-1)#?

Question

Ethan Adkins · Accepted Answer

The domain of #y# is #D_y=RR-{1}#
The range of #y# is #R_y=RR-{0}# As you cannot divide by #0#, #x!=1# The domain of #y# is #D_y=RR-{1}# To find the range, we need #y^-1# #y=2/(x-1)# #(x-1)y=2# #xy-y=2# #xy=y+2# #x=(y+2)/y# Consequently, #y^-1=(x+2)/x# The domain of #y^-1=RR-{0}# This is the range of #y# The range of #y# is #R_y=RR-{0}#

Jace Anderson · Answer

undefined To find the domain of $ y = \frac{2}{x-1} $, we identify any values of $ x $ that would make the denominator $ x - 1 $ equal to zero. So, the domain is all real numbers except $ x = 1 $.

To find the range, we consider what values $ y $ can take. As $ x $ approaches 1 from either side, $ y $ approaches positive or negative infinity. Hence, the range of $ y $ is all real numbers except $ y = 0 $.

Kennedy Adams · Answer

undefined To find the domain and range of the function $y = \frac{2}{x-1}$:

Domain:
The function is defined for all real numbers except when the denominator $x - 1$ equals zero because division by zero is undefined. Therefore, the domain is all real numbers except $x = 1$. In interval notation, the domain is $(- \infty, 1) \cup (1, +\infty)$.

Range:
The range of the function can be determined by considering the behavior of the function as $x$ approaches positive infinity and negative infinity. As $x$ approaches positive infinity, the function approaches $0^+$. As $x$ approaches negative infinity, the function approaches $0^-$. Since $0$ is included in the range and the function never equals $0$, the range is all real numbers except $0$. In interval notation, the range is $(- \infty, 0) \cup (0, +\infty)$.